Bllisti Mjorn nnowire evies Öner Gül,,,, Ho Zhng,,, Jouri D.S. Bommer,, Mihiel W.A. e Moor, Din Cr, Séstien R. Plissr,, Erik P.A.M. Bkkers,, Attil Geresi, Kenji Wtne, 3 Tkshi Tniguhi, 3 Leo P. Kouwenhoven,4, QuTeh n Kvli Institute of Nnosiene, Delft University of Tehnology, 6 GA Delft, The Netherlns Deprtment of Applie Physis, Einhoven University of Tehnology, 56 MB Einhoven, The Netherlns 3 Avne Mterils Lortory, Ntionl Institute for Mterils Siene, - Nmiki, Tsuku, 35-44, Jpn 4 Mirosoft Sttion Q Delft, 6 GA Delft, The Netherlns lrey een relize in semionutor nnowires, fulfilling the further requirements for Mjorn quits. However, espite these vnes in mterils, lterntive explntions hve een propose for the hrteristi Mjorn signtures. Most lterntive explntions invoke ulk or interfe isorer 6 or nonuniform hemil potentil long the wire,3. Notle exmples re wek ntiloliztion 4, Kono effet 5, n Anreev levels 6,, ll shown to result in trnsport signtures mimiking those ttriute to Mjorns. Here, we show hrteristi Mjorn signtures in nnowire evies tht exhiit llisti trnsport, ruling out ll known isorer- or nonuniformity-se explntions for the first time. Figure shows the mesure evie onsisting of n InS nnowire (green) ontte with groune NTiN superonutor (purple), n norml metl les (yellow). The lol ottom gte eletroes re seprte from the nnowire y oron nitrie flke n re operte iniviully to llow for sptil ontrol of the rrier ensity in the nnowire. We hve relize our evies following our reently evelope nnofrition reipe whih results in high-qulity InS NTiN interfe, hr inue superonuting gp, n llisti trnsport in the proximitize nnowire (see Ref. 9 n ). All mesurements re performe in ilution refrigertor with n eletron temperture of 5 mk. The t is tken y pplying is voltge V etween the norml metl le n the superonutor inite y N n S, respetively, n monitoring the urrent flow. The other norml le is kept floting. Figure shows the ifferentil onutne I/V while vrying V, n stepping the voltge pplie to the rrier gte. Importntly, we fin no signs of formtion of quntum ots or ny other loliztion effets. Vertil line uts t the gte voltges inite with olore rs re shown in Figure. Figure (ottom) is from the tunneling regime of the evie where suffiiently negtive voltge on rrier gte lolly epletes the nonovere nnowire setion, n retes tunnel rrier etween the norml le n the superonutor. In this regime we fin n inue superonuting gp with strong onutne suppression for sugp is. The extrte gp vlue is =.65 mev. Inresing the voltge on rrier gte first lowers the tunnel rrier n then removes it ompletely. Figure (top) is from the regime in whih the nonovere nnowire setion mits sinrxiv:63.469v [on-mt.mes-hll] De 7 Mjorn moes re zero-energy exittions of topologil superonutor tht exhiit non- Aelin sttistis 3. Following proposls for their etetion in semionutor nnowire ouple to n s-wve superonutor 4,5, severl tunneling experiments reporte hrteristi Mjorn signtures 6. Reuing isorer hs een prime hllenge for these experiments euse isorer n mimi the zero-energy signtures of Mjorns 6, n reners the topologil properties inessile 7. Here, we show hrteristi Mjorn signtures in InS nnowire evies exhiiting ler llisti trnsport properties. Applition of mgneti fiel n sptil ontrol of rrier ensity using lol gtes genertes zero is pek tht is rigi over lrge region in the prmeter spe of hemil potentil, Zeemn energy, n tunnel rrier potentil. The reution of isorer llows us to resolve seprte regions in the prmeter spe with n without zero is pek, initing topologilly istint phses. These oservtions re onsistent with the Mjorn theory in llisti system, n exlue for the first time the known lterntive explntions tht invoke isorer 6 or nonuniform hemil potentil,3. Semionutor nnowires re the primry ontener for relizing topologil quntum it (quit) se on Mjorn moes. Their onfine geometry together with the highly tunle eletroni properties reily llow for lolizing Mjorns, engineering the oupling etween Mjorns, n finlly ontrolling the oupling etween the topologil superonutor n the externl iruity. These requirements for the implementtion of Mjorn quit re hllenging to hieve in other Mjorn systems suh s D n 3D topologil insultors. Moreover, vrious si networks 4 n highqulity interfes to ifferent superonutors 8 hve These uthors ontriute eqully to this work. Corresponene to Ö.G. (oner gul@g.hrvr.eu) or H.Z. (h.zhng-3@tuelft.nl) or L.P.K. (l.p.kouwenhoven@tuelft.nl) Present ress: Deprtment of Physis, Hrvr University, Cmrige, MA 38, USA Present ress: CNRS-Lortoire Anlyse et Arhiteture es Systèmes (LAAS), Université e Toulouse, 7 venue u olonel Rohe, F-34 Toulouse, Frne
N S norml gte super gte rrier gte μm - - -.6 Voltge on rrier gte (V) -.5 V > Δ* V =.5 - - -.6 Voltge on rrier gte (V) -.5 Figure. Hyri evie n llisti trnsport properties., Flse-olor eletron mirogrph of the mesure evie. The InS nnowire (green) is ontte y groune NTiN superonutor (purple) n two Au norml metl les (yellow). The nnowire hs imeter of 8 nm. The lol ottom gtes (norml, rrier, n super gte) re seprte from the nnowire y oron nitrie flke ( 3 nm) n re operte iniviully. Two-terminl mesurements re performe etween N n S, while the other norml le is floting., Differentil onutne I/V s funtion of is voltge V, n voltge on rrier gte (the other gte eletroes re groune). Vertil lines t ertin gte voltges re ue to slow flututions in the eletrostti environment., Vertil line uts from t the gte voltges mrke with olore rs. Top pnel shows the I/V from the trnsport regime in whih the urrent is rrie y single fully-trnsmitting hnnel. We fin n enhnement of onutne t smll is y more thn ftor of.5 ompre to the lrge-is onutne of e /h. Bottom pnel is from the tunneling regime in whih the urrent is rrie y single hnnel with low trnsmission. We extrt n inue superonuting gp =.65 mev., Horizontl line uts from t the is voltges mrke with olore rs. Sugp onutne (V = ) shows n enhnement rehing.5 e /h when the lrge-is onutne (V =.4 mv > ) hs quntize vlue of e /h. gle fully-trnsmitting trnsport hnnel. In this regime the sugp onutne is strongly enhne ue to Anreev refletion ompre to the lrge-is (ove-gp) onutne of e /h. The extrte enhnement ftor >.5 implies ontt interfe trnspreny >.93. Figure shows the horizontl line uts from Figure t the is voltges inite with olore rs. For is V > we fin quntize onutne plteu t e /h, ler signture of llisti evie. For zero is voltge the strong Anreev enhnement is evient in the plteu region followe y ip in onutne ue to hnnel mixing. From the sene of quntum ots, the oserve inue gp with strongly reue sugp ensity of sttes, high interfe trnspreny, n quntize onutne, we onlue very low isorer strength for our evie, onsistent with our reent finings. We now turn to the tunneling regime of the evie where Mjorn moes re hrterize y zero is pek. To rive the nnowire evie into the topologil phse, we pply mgneti fiel B long the wire xis n tune the voltge pplie to the super gte (V s gte ) whih ontrols µ, the hemil potentil in the nnowire setion unerneth the superonutor. Figure shows
3.5.3 V s-gte =.75 V.3..7 T.5.5.5 E Z = μ B g InS B (mev) -.3 -.4 Voltge on norml gte (V).8.7.3.7 T -.3 -.5 Voltge on rrier gte (V) -..5.3.7 T -.5.5 -.3 - Voltge on super gte (V). Figure. Zero is pek n its epenene on mgneti fiel n lol gte voltges., Differentil onutne I/V s funtion of is voltge V, n n externl mgneti fiel B long the nnowire xis for V s gte =.75 V. The mgneti fiel loses the inue gp t.55 T n genertes zero is pek whih persists up to. T. The right xis sles with Zeemn energy E z ssuming g ftor of 4 otine inepenently 5,6. (Voltge on norml n rrier gte: V n.4 V), I/V s funtion of V n voltge on norml gte. The voltge on norml gte hnges the onutne y more thn ftor of 5 ut oes not ffet the presene of the zero is pek., I/V s funtion of V n voltge on rrier gte. The voltge on rrier gte hnges the onutne y nerly n orer of mgnitue ut oes not ffet the presene of zero is pek., I/V s funtion of V n voltge on super gte. The zero is pek persists for finite gte voltge rnge. The lue r inites the voltge on super gte in, n. Voltge on rrier gte is juste to keep the overll onutne the sme when sweeping the voltge on super gte. tht n inresing B loses the inue gp t.55 T n genertes zero is pek rigily oun to V = up to. T (line uts in Suppl. Figure ). The gp losure is expete to our for Zeemn energy E z. From liner interpoltion we fin g 4 whih mthes our inepenent mesurements 5,6. Converting the B xis into Zeemn energy E z sle (right vertil xis), we fin tht the zero is pek is oun to zero over.75 mev, rnge in Zeemn energy tht is 3 times lrger thn the pek with (the full with t hlf mximum, FWHM µev, see Suppl. Figure n Suppl. Figure 4). This exlues level rossing s the origin for our zero is pek 5. We note tht ll our evies show signifint inrese of sugp ensity of sttes for the mgneti fiels require for topologil phse trnsition. This ehvior is likely ue to vortex formtion or short men free pth 7,8 in our NTiN film, n is sujet of our future stuies. The formtion of vorties is speulte to rete issiption hnnel, the leing hypothetil mehnism tht limits our zero is pek height from rehing the quntize vlue of e /h. An unmiguous oservtion of zero is pek quntiztion remins n outstning hllenge for Mjorn experiments in semionutor nnowires. The origin of zero is pek n e sptilly resolve y vrying the voltges pplie to iniviul gtes. Figure shows tht the presene of the zero is pek is not ffete when gting the wire setion unerneth the
4 z..6.5 V s-gte =.75 V B SO φ y x..8.5 V s-gte =.75 V -.5.5 B y (T) I/V (e /h) -..575 T -5. º φ (º).3 5 º 5.5.8 -.. -.. Figure 3. Depenene of zero is pek on mgneti fiel orienttion., Orienttion of the nnowire evie. The wire is long x n the spin orit fiel B so is long y. The sustrte plne is spnne y x n y. ϕ is the ngle etween the x xis n the orienttion of the externl mgneti fiel in the plne of the sustrte., Differentil onutne I/V s funtion of is voltge V, n n externl mgneti fiel long the y xis. Applition of mgneti fiel long B so loses the inue gp ut oes not generte zero is pek., I/V s funtion of V, n in-plne rottion of the mgneti fiel with mgnitue of.575 T. The zero is pek ppers in n ngle rnge in whih the externl mgneti fiel is mostly ligne with the wire. We ttriute the low onutne region roun the zero is pek to the inue gp. Orienting the mgneti fiel wy from the wire xis n more towrs B so loses the inue gp n splits the zero is pek (see line uts in )., Vertil line uts from t the ngles inite with olore rs. For ϕ = the zero is pek is present, whih is split for ϕ = 5. norml ontt whih hnges the onutne y more thn ftor of 5 (see lso Suppl. Figure ). Extening the sme nlysis to the nonovere wire setion yiels the sme result (Figure ), i.e., hnging the tunnel rrier onutne y nerly n orer of mgnitue oes not split the zero is pek, nor mkes it ispper (see lso Suppl. Figure e). In ontrst, Figure shows tht the zero is pek is present over finite rnge in voltge pplie to the super gte (line uts in Suppl. Figure f). This inites tht proper tuning of µ is essentil for the pperne of the zero is pek. The oservtion of zero is pek tht oes not split when hnging the tunnel rrier onutne (Figure ) exlues Kono effet 5 n rossing of Anreev levels 6 s the origin of our zero is pek. Most importntly, it rules out n explntion provie y reent theory work emonstrting trivil Anreev levels lolize ner the nonovere wire setion tht re oun to zero energy for vrying E z n µ, ut quikly split to finite energies for vrying tunnel rrier strength. Here we emonstrte for the first time zero is pek rigily oun to V = over hnging tunnel rrier onutne ehvior oserve in ll evies (Suppl. Figure 5-7). From the omine nlysis (Figure -) we onlue tht the zero is pek origintes in the wire setion unerneth the superonutor, onsistent with Mjorn interprettion. In Mjorn nnowire 4,5, the existene of topologil phse stritly requires n externl mgneti fiel with finite omponent perpeniulr to the spin orit fiel B so, see Figure 3. An externl fiel long the wire fulfills this requirement, shown in Figure. In ontrst, Figure 3 shows tht n externl mgneti fiel prllel to B so oes not generte zero is pek for the sme gte settings in Figure. Figure 3 shows the epenene of the zero is pek on the iretion of the externl fiel. The zero is pek is limite to n ngle rnge where the externl fiel is mostly ligne with the wire, perpeniulr to B so (see Suppl. Figure for mesurement in lrger ngle rnge). We oserve low onutne region roun the zero is pek, initing the inue gp. Orienting the mgneti fiel wy from the wire xis n more towrs B so loses the inue gp n splits the zero is pek. This is inite y the vertil line uts from Figure 3 t mrke ngles, shown in Figure 3. A gp losing is expete for the ritil n-
5 I/V (e/h)..5 T Vs-gte = -7 V. I/V (e/h) EZ = μb gins B (mev).8.4 - I/V (e/h) Vs-gte = - V -.. e EZ = μb gins B (mev) T T. T - zero is pek no zero is pek - - -9-8 -7-6 -5-4 -3 - - Vs-gte (V) EZ = μb gins B (mev) Figure 4. Zero is pek n phse igrm., Differentil onutne I/V of nother evie mesure s funtion of is voltge V, n n externl mgneti fiel B long the nnowire xis. We fin n inue gp =.9 mev t zero mgneti fiel. Inresing the mgneti fiel loses the inue gp t T n genertes zero is pek tht persists up to t lest.5 T. The right xis sles with Zeemn energy Ez ssuming gins = 4 otine inepenently5,6. The purple rrow t. T inites the onset of the zero is pek., Line uts from with. e /h offset., Line uts from n t n. T., Sme s ut with ifferent super gte voltge Vs gte = V. For this super gte voltge, the onset of the zero is pek is t lrger mgneti fiel of.66 T, s mrke y purple rrow. e, Phse igrm onstrute y the onset n the en of the zero is pek in mgneti fiel for ifferent super gte voltges. The purple squres enote the onset, pink the en. For Vs gte = 3 V no zero is pek is oserve.
6 gle ϕ given y the projetion rule 9,3 E z sin(ϕ ) =. From the oserve gp = 75 µev t B =.575 T n g ftor of 4, we otin ϕ = 5, greeing well with the oserve vlue of ϕ ( reution in ϕ is expete ue to oritl effet of the externl mgneti fiel 3 ). Finlly, in Suppl. Figure we show tht inresing B ereses ϕ, ehvior onsistent with the projetion rule. We now turn our ttention to n ientil evie ut with longer proximitize wire setion (. µm, see Suppl. Figure 3). Figure 4- show n inue gp =.9 mev t zero mgneti fiel, signifintly lrger thn the evie in Figure -3. As result, the inue gp loses t higher mgneti fiel ( T). The zero is pek is visile n unsplit over rnge of t lest.3 T, orresponing to Zeemn energy sle >.5 mev. The FWHM is roun.7 mev yieling rtio ZBP-rnge/FWHM (Suppl. Figure 4). A isorer-free Mjorn theory moel with prmeters extrte from this evie (geometry, inue gp, spin orit oupling, temperture) fins perfet greement etween simultion n our t (Figure 4). Suppl. Figure 3 n shows tht the zero is pek position is roust ginst hnge in onutne when vrying the voltge pplie to the norml n the rrier gte, ruling out the trivil Anreev-level explntion onsistent with our erlier isussion (Figure n ). In ontrst to norml n rrier gte, the voltge pplie to the super gte hnges the onset n the en of the zero is pek in mgneti fiel. Figure 4 shows tht for V s gte = V the zero is pek ppers t higher mgneti fiel ompre to Figure 4 where V s gte = 7 V (.66 T vs.. T). We hve extene this nlysis for V V s gte V n mrke the mgneti fiel vlues t whih the zero is pek strts n ens (Suppl. Figure 3). The resulting phse igrm is shown in Figure 4e. For lrge negtive voltges pplie to the super gte, we fin region in whih the zero is pek persists for lrge rnges of mgneti fiel n V s gte, initing the topologil phse. We ttriute the pperne of trivil phse t lrge mgneti fiels ove the topologil phse to multi-hnnel ouption in the proximitize wire setion,. A preise knowlege of the phse ounries requires theory inluing finite-size effets 3, the oritl effet of the mgneti fiel 3, n n urte eletrostti moeling of the evie 33, n will e resse in future stuies. In onlusion, the presente experiments emonstrte zero is peks over n extene rnge in Zeemn energy n gte voltge in evies tht show ler llisti trnsport properties, n revel the istint phses in the topology of Mjorn wires. These oservtions exlue ll known lterntive explntions for our zero is peks tht re se on isorer. Methos Nnowire growth n evie frition. InS nnowires hve een grown y Au-tlyze Vpor- Liqui-Soli mehnism in Metl Orgni Vpor Phse Epitxy retor. The InS nnowires re zin lene, long [] rystl iretion, n re free of stking fults n islotions 34. As-grown nnowires re eposite one-y-one using miro-mnipultor 35 on sustrte ptterne with lol gtes overe y 3 nm thik hbn ieletri. The ontt eposition proess strts with resist evelopment followe y oxygen plsm lening. Then, the hip is immerse in sulfur-rih mmonium sulfie solution ilute y wter (with rtio of :) t 6 C for hlf n hour 36. At ll stges re is tken to expose the solution to ir s little s possile. For norml metl ontts 5,6, the hip is ple into n evportor. A 3 seon helium ion milling is performe in situ efore evportion of Cr/Au ( nm/5 nm) t se pressure < 7 mr. For superonuting ontts 9,, the hip is mounte in sputtering system. After 5 seons of in situ rgon plsm ething t power of 5 Wtts n pressure of mtorr, 5 nm NTi is sputtere followe y 85 nm NTiN. Dt vilility. All t re ville t oi.org/.4/uui:3f9937-8-4f8-84-5f5777 (Ref. 37). Re, N. & Green, D. Pire sttes of fermions in two imensions with reking of prity n time-reversl symmetries n the frtionl quntum Hll effet. Phys. Rev. B 6, 67 () Kitev, A. Y. Unpire Mjorn fermions in quntum wires. Phys. Usp. 44, 3-36 () 3 Fu, L. & Kne, C. L. Superonuting proximity effet n Mjorn fermions t the surfe of topologil insultor. Phys. Rev. Lett., 9647 (8) 4 Luthyn, R. M., Su, J. D. & Ds Srm, S. Mjorn fermions n topologil phse trnsition in semionutor-superonutor heterostrutures. Phys. Rev. Lett. 5, 77 () 5 Oreg, Y., Refel, G. & von Oppen, F. Helil liquis n Mjorn oun sttes in quntum wires. Phys. Rev. Lett. 5, 77 () 6 Mourik, V. et l. Signtures of Mjorn fermions in hyri superonutor-semionutor nnowire evies. Siene 336, 3-7 () 7 Ds, A. et l. Zero-is peks n splitting in n Al-InAs nnowire topologil superonutor s signture of Mjorn fermions. Nture Phys. 8, 887-895 () 8 Deng, M. T. et l. Anomlous zero-is onutne pek in N InS nnowire N hyri evie. Nno Lett.,
7 644-649 () 9 Alreht, S. M. et l. Exponentil protetion of zero moes in Mjorn islns. Nture 53, 6-9 (6) Deng, M. T. et l. Mjorn oun stte in ouple quntum-ot hyri-nnowire system. Siene 354, 557-56 (6) Chen, J. et l. Experimentl phse igrm of zerois onutne peks in superonutor/semionutor nnowire evies. Si. Av. 3, e7476 (7) Liu, J., Potter, A. C., Lw, K. T. & Lee, P. A. Zero-is peks in the tunneling onutne of spin-orit-ouple superonuting wires with n without Mjorn ensttes. Phys. Rev. Lett. 9, 67 () 3 Bgrets, D. & Altln, A. Clss D spetrl pek in Mjorn quntum wires. Phys. Rev. Lett. 9, 75 () 4 Pikulin, D. I., Dhlhus, J. P., Wimmer, M., Shomerus, H. & Beenkker, C. W. J. A zero-voltge onutne pek from wek ntiloliztion in Mjorn nnowire. New J. Phys. 4, 5 () 5 Lee, E. J. H. et l. Zero-Bis nomly in nnowire quntum ot ouple to superonutors. Phys. Rev. Lett. 9, 868 () 6 Lee, E. J. H. et l. Spin-resolve Anreev levels n prity rossings in hyri superonutor-semionutor nnostrutures. Nture Nnoteh. 9, 79-84 (4) 7 Tkei, S., Fregoso, B. M., Hui, H.-Y., Loos, A. M. & Ds Srm, S. Soft superonuting gp in semionutor Mjorn nnowires. Phys. Rev. Lett., 8683 (3) 8 Chng, W. et l. Hr gp in epitxil semionutorsuperonutor nnowires. Nture Nnoteh., 3-36 (5) 9 Gül, Ö. et l. Hr superonuting gp in InS nnowires. Nno Lett. 7, 69-696 (7) Zhng, H. et l. Bllisti superonutivity in semionutor nnowires. Nture Commun. 8, 65 (7) Liu, C.-X., Su, J. D. & Ds Srm, S. Role of issiption in relisti Mjorn nnowires. Phys. Rev. B 95, 545 (7) Liu, C.-X., Su, J. D., Stnesu, T. D. & Ds Srm, S. Anreev oun sttes versus Mjorn oun sttes in quntum ot-nnowire-superonutor hyri strutures: Trivil versus topologil zero-is onutne peks. Phys. Rev. B 96, 756 (7) 3 Pr, E., Sn-Jose, P. & Aguo, R. Trnsport spetrosopy of NS nnowire juntions with Mjorn fermions. Phys. Rev. B 86, 853(R) () 4 Gziegovi, S. et l. Epitxy of vne nnowire quntum evies. Nture 548, 434-438 (7) 5 Kmmhuer, J. et l. Conutne quntiztion t zero mgneti fiel in InS nnowires. Nno Lett. 6, 348-3486 (6) 6 Kmmhuer, J. et l. Conutne through helil stte in n inium ntimonie nnowire. Nture Commun. 8, 478 (7) 7 Cole, W. S., Su, J. D. & Ds Srm, S. Proximity effet n Mjorn oun sttes in len semionutor nnowires ouple to isorere superonutors. Phys. Rev. B 94, 555(R) (7) 8 Stnesu, T. D. & Ds Srm, S. Proximity-inue low-energy renormliztion in hyri semionutorsuperonutor Mjorn strutures. Phys. Rev. B 96, 45 (7) 9 Os, J., Ruiz, D., & Serr, L. Effets of tilting the mgneti fiel in one-imensionl Mjorn nnowires. Phys. Rev. B 89, 4545 (4) 3 Rex, S. & Suø, A. Tilting of the mgneti fiel in Mjorn nnowires: ritil ngle n zero-energy ifferentil onutne. Phys. Rev. B 9, 549 (4) 3 Nijholt, B. & Akhmerov, A. R. Oritl effet of mgneti fiel on the Mjorn phse igrm. Phys. Rev. B 93, 35434 (6) 3 Mishmsh, R. V., Asen, D., Higginothm, A. P. & Alie, J. Approhing topologil phse trnsition in Mjorn nnowires. Phys. Rev. B 93, 4544 (6) 33 Vuik, A., Eeltink, D., Akhmerov, A. R. & Wimmer, M. Effets of the eletrostti environment on the Mjorn nnowire evies. New J. Phys. 8, 333 (6) 34 Cr, D., Wng, J., Verheijen, M. A., Bkkers, E. P. A. M. & Plissr, S. R. Rtionlly esigne single-rystlline nnowire networks. Av. Mter. 6, 4875-4879 (4) 35 Flöhr, K. et l. Mnipulting InAs nnowires with sumirometer preision. Rev. Si. Instrum. 8, 375 () 36 Suytin, D. B., Thelner, C., Björk, M. T., Mximov, I. & Smuelson, L. Sulfur pssivtion for ohmi ontt formtion to InAs nnowires. Nnotehnology 8, 537 (7) 37 Gül, Ö. et l. Bllisti Mjorn nnowire evies. 4TU.ReserhDt. Aville t oi.org/.4/uui: 3f9937-8-4f8-84-5f5777 (7) Aknowlegments We thnk A.R. Akhmerov, O.W.B. Benningshof, M.C. Cssiy, S. Goswmi, J. Kmmhuer, V. Mourik, M. Quintero-Pérez, J. Shen, M. Wimmer, D.J. vn Woerkom, n K. Zuo for isussions n ssistne. This work hs een supporte y the Netherlns Orgnistion for Sientifi Reserh (NWO), Europen Reserh Counil (ERC), n Mirosoft Corportion Sttion Q. Author ontriutions Ö.G., H.Z., n J.D.S.B frite the evies, performe the mesurements, n nlyze the t. M.W.A..M. ontriute to the evie frition. D.C., S.R.P. n E.P.A.M.B. grew the InS nnowires. A.G. ontriute to the experiments. K.W. n T.T. synthesize the hbn rystls. L.P.K. supervise the projet. Ö.G., H.Z., n J.D.S.B. o-wrote the pper. All uthors ommente on the mnusript.
8 Supplementry Informtion: Bllisti Mjorn nnowire evies Öner Gül,, Ho Zhng,, Jouri D.S. Bommer, Mihiel W.A. e Moor, Din Cr, Séstien R. Plissr, Erik P.A.M. Bkkers, Attil Geresi, Kenji Wtne, Tkshi Tniguhi, Leo P. Kouwenhoven These uthors ontriute eqully to this work. Corresponene to Ö.G. (oner gul@g.hrvr.eu) or H.Z. (h.zhng-3@tuelft.nl) or L.P.K. (l.p.kouwenhoven@tuelft.nl) List of supplementry figures Supplementry Figure Line uts from min text Figure. Supplementry Figure Depenene of the zero is pek on the orienttion of n in-plne mgneti fiel. Supplementry Figure 3 Zero is pek in lrge rnge of mgneti fiel n lol gte voltges. Supplementry Figure 4 Zero is pek height n with. Supplementry Figure 5 Aitionl evie - llisti trnsport properties. Supplementry Figure 6 Aitionl evie - zero is pek in lrge rnge of mgneti fiel n lol gte voltges. Supplementry Figure 7 Aitionl evie - zero is pek in lrge rnge of mgneti fiel n lol gte voltges.
9 rrier gte voltge = -.4 V.5 T.6 rrier gte voltge = -.5 V.5 T.8.6.4.4.. T.5.5 T.5.5.5 μev.. T.. e f norml gte.8 V rrier gte -. V super gte.6. V.5..4.5.. -.4 V -.5 V - V.3.3.3.3.3.3
Supplementry Figure Line uts from min text Figure., Line uts from min text Figure with. e /h offset. An inresing mgneti fiel loses the inue gp t.55 T n genertes zero is pek up to. T., Sme s ut for lrger tunnel rrier strength. Offset:.6 e /h., Line ut from. T. We fin the full with t hlf mximum of the zero is pek to e µev., Line uts from min text Figure in logrithmi sle (without offset). A vrition in voltge on the norml gte (.4 V V n gte.8 V) hnges the onutne y more thn ftor of 5, ut oes not remove the zero is pek. e, Line uts from min text Figure in logrithmi sle (without offset). A vrition in voltge on the rrier gte (.5 V V gte. V) hnges the onutne y nerly n orer of mgnitue, ut oes not remove the zero is pek. f, Line uts from min text Figure with.6 e /h offset. A vrition in voltge on the super gte ( V V s gte. V) ffets the presene of the zero is pek, whih is stle for finite gte voltge rnge.
.4 V s-gte =.75 V.6.5 -.4.6 T -9-6 -3 3 6 9 φ (º). V s-gte =.75 V.6.5..575 T.65 T -...575 T V s-gte =.75 V.5 º º.3 º º.8.4 5 º 5 º -..65 T -5 φ (º) 5.9 -.. -.. Supplementry Figure Depenene of the zero is pek on the orienttion of n in-plne mgneti fiel., Differentil onutne I/V s funtion of is voltge V, n in-plne rottion of the mgneti fiel with mgnitue of.6 T. ϕ = orrespons to n externl fiel long the wire, ϕ = ±9 to n externl fiel prllel to the spin orit fiel B so. The zero is pek is present in n ngle rnge ( ϕ < ) when the externl mgneti fiel is mostly ligne with the wire. We oserve low onutne region roun the zero is pek, initing the inue gp. Orienting the mgneti fiel wy from the wire xis n more towrs B so loses the inue gp n splits the zero is pek. We o not oserve stle zero is pek for ϕ > in the entire ngle rnge. The she squre inites the ngle rnge shown in min text Figure 3.,, I/V s funtion of V, n in-plne rottion of the mgneti fiel with two ifferent mgnitues. Inresing the mgneti fiel ereses the ngle rnge of the zero is pek (ompre n )., Vertil line uts from n t the ngles inite with olore rs. Top pnels: For ϕ = the zero is pek is present for oth mgneti fiel mgnitues. Bottom pnels: For ϕ = 5 no zero is pek is present for oth mgnitues. Mile pnels: For ϕ = the zero is pek is present only for.575 T, while is split for.65 T.
.3 B.35 T -.3 N S 5 Voltge on norml gte (V) super gte.3 norml gte rrier gte I/V (e/h).5 Vs-gte = -6.5 V μm I/V (e/h).5 Vs-gte = -6.5 V.35 T -.3 -.4 -.63 Voltge on rrier gte (V) - - Vs-gte= -5 V - Vs-gte= I/V - V (e/h) - - - Vs-gte= -3 V - - Vs-gte= I/V V (e/h). - Vs-gte= I/V - V (e/h). Vs-gte= -4 V Vs-gte= I/V -7 V (e/h). - Vs-gte= -6 V Vs-gte= -8 V Vs-gte= -9 V Vs-gte= - V. -
Supplementry Figure 3 Zero is pek in lrge rnge of mgneti fiel n lol gte voltges., Flse-olor eletron mirogrph of the mesure evie.,, Differentil onutne I/V s funtion of is voltge V, n voltges on norml n rrier gte, respetively. A vrition in eh gte voltge hnges the onutne y n orer of mgnitue, ut oes not ffet the presene of the zero is pek., I/V s funtion of V n n externl mgneti fiel B long the nnowire xis, mesure t ifferent voltges on super gte ( V V s gte V). A vrition in V s gte hnges the mgneti fiel rnge in whih the zero is pek ppers. The purple (pink) rrows inite the onset (en) of the zero is pek in externl mgneti fiel. When hnging the super gte voltge, we just the tunnel gte voltge to keep the overll onutne the sme. 3
4 Fig. Fig. 4. zero is onutne reltive height. zero is onutne reltive height.5.5 FWHM (mev) FWHM (mev).5.5..5.5..5..5 Supplementry Figure 4 Zero is pek height n with., The solute n the reltive height of the zero is pek extrte from min text Figure. The ifferene etween the solute n the reltive height is the sugp onutne roun zero is for eh mgneti fiel., The full with t hlf mximum (FWHM) of the zero is pek extrte from min text Figure.,, Sme s n ut for the zero is pek from min text Figure 4.
5 norml gte rrier gte super gte N S -.5 μm - -.88 Voltge on rrier gte (V).3.5 V > Δ* V ~ - - -.88 Voltge on rrier gte (V).3 Supplementry Figure 5 Aitionl evie - llisti trnsport properties., Flse-olor eletron mirogrph of the mesure evie., Differentil onutne I/V s funtion of is voltge V, n voltge on rrier gte., Vertil line uts from t the gte voltges mrke with olore rs. Top pnel shows the I/V from the trnsport regime in whih the urrent is rrie y single fully-trnsmitting hnnel. We fin n enhnement of onutne t smll is y ftor of.5 ompre to the lrge-is onutne of e /h. Bottom pnel is from the tunneling regime. We extrt n inue superonuting gp =.75 mev., Horizontl line uts from t the is voltges mrke with olore rs. Lrge-is onutne (V = mv > ) shows quntize plteu of e /h. The sugp onutne (V =.5 mv) is enhne within the gte voltge rnge in whih the lrge-is onutne is quntize. We exlue series resistne of.5 kω, solely to ount for the ontt resistne of the norml le S,S.
6.75. V s-gte = -. V.7.5.45.5 T.75.5.5.5.5 E Z = μ B g InS B (mev) -.7 - Voltge on norml gte (V).5.7..8.5 T -.7 -.45 Voltge on rrier gte (V).4.5...5 T f -.5.75 V s-gte = -.9 V V s-gte =.9 V.5 e -. -.5 Voltge on super gte (V).35.5 T -.5 -.5 Voltge on super gte (V) 5 -.5.5 -.5.5
Supplementry Figure 6 Aitionl evie - zero is pek in lrge rnge of mgneti fiel n lol gte voltges., Differentil onutne I/V s funtion of is voltge V, n n externl mgneti fiel B long the nnowire xis. Applition of mgneti fiel genertes zero is pek t.3 T. The zero is pek persists up to.7 T n splits for lrger mgneti fiels. The right xis sles with Zeemn energy E z ssuming g ftor of 4., I/V s funtion of V n voltge on the norml gte. The voltge on the norml gte hnges the onutne y ftor of ut oes not ffet the presene of the zero is pek., I/V s funtion of V n voltge on the rrier gte. The voltge on the rrier gte hnges the onutne y ftor of ut oes not ffet the presene of the zero is pek., I/V s funtion of V n voltge on the super gte. The zero is pek is stle for finite rnge of voltges on the super gte. e, Sme s ut t zero mgneti fiel. No zero is pek is present. f, Sme s ut for ifferent voltges on the super gte (V s gte ). No zero is pek is present for the mesure mgneti fiel rnge for V s gte =.9 V n V s gte =.9 V, onsistent with. 7
8 norml gte B rrier gte super gte.5.4 T.5.45 N S μm -.5-5 Voltge on norml gte (V).45.5.4 T.5.5.5.5 E Z = μ B g InS B (mev) e -.5-6.5-5 Voltge on rrier gte (V).5.45.5.46 T -.5.5 -.5-3. -. Voltge on super gte (V) Supplementry Figure 7 Aitionl evie - zero is pek in lrge rnge of mgneti fiel n lol gte voltges., Flse-olor eletron mirogrph of the mesure evie., Differentil onutne I/V s funtion of is voltge V n mgneti fiel B. Inresing the mgneti fiel loses the gp n genertes zero is pek whih persists up to t lest T. The right xis sles with Zeemn energy ssuming g InS = 4. Gte voltges re fixe t V n gte = V, V gte = 5.5 V, n V s gte =.8 V for norml, rrier, n super gte, respetively., I/V s funtion of V, n norml gte voltge V n gte. A lrge vrition in V n gte n moulte the overll onutne ut it oes not remove the zero is pek. Tken t B =.4 T, V gte = 5.5 V, n V s gte =.85 V., I/V s funtion of V, n rrier gte voltge. Chnging the tunnel rrier onutne y more thn ftor of 3 oes not split the zero is pek, nor mkes it ispper. Tken t V n gte =.5 V n V s gte =.85 V.
e, I/V s funtion of V, n super gte voltge V s gte. The zero is pek is stle over finite rnge in V s gte. Tken t V n gte = V n V gte = 5.5 V. 9 [S] Zhng, H. et l. Bllisti superonutivity in semionutor nnowires. Nture Commun. 8, 65 (7) [S] Kmmhuer, J. et l. Conutne quntiztion t zero mgneti fiel in InS nnowires. Nno Lett. 6, 348-3486 (6)